a water storage tank is shaped like a cone. the diameter of the circular base of the tank is 4.5 feet, and the height of the tank is 9 feet. if the tank can be drained at a rate of 2 cubic feet per second, how long will it take to drain it completely? 35 4 seconds 71 7 seconds 23.9 seconds 21.2 seconds

Question

Accepted Answer

# Explanation:
## Step1: Calculate the radius of the cone
The diameter $d = 4.5$ feet. The radius $r=\frac{d}{2}=\frac{4.5}{2}=2.25$ feet.
## Step2: Use the volume formula for a cone $V=\frac{1}{3}\pi r^{2}h$
Substitute $r = 2.25$ feet and $h = 9$ feet into the formula.
$$
\begin{align*}
V&=\frac{1}{3}\times\pi\times(2.25)^{2}\times9\
&=\pi\times(2.25)^{2}\times3\
&=\pi\times5.0625\times 3\
&=15.1875\pi\
&\approx15.1875\times3.14\
& = 47.68875
\end{align*}
$$
## Step3: Calculate the time to drain the tank
The rate of draining is $2$ cubic feet per second. Time $t=\frac{V}{rate}$.
$t=\frac{47.68875}{2}=23.844375\approx23.9$ seconds

# Answer:
23.9 seconds

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the radius of the cone

Step2: Use the volume formula for a cone \(V=\frac{1}{3}\pi r^{2}h\)

Step3: Calculate the time to drain the tank

Answer: